Tuning graphene’s properties through structural design has received significant attention. However, the complex nonlinear relationship between geometric parameters of structural design and performance needs further exploring to accurately predict the performance of graphene and speed up the optimization of its structural design. This study introduces periodic rhombic perforations to effectively achieve the structural design of graphene with negative Poisson’s ratio (NPR). The mechanisms underlying the NPR effect are analyzed, and a data-driven machine learning model based on a backpropagation neural network (BPNN) is developed to efficiently predict and design perforated graphene structures exhibiting NPR. By constructing a Poisson’s ratio dataset for rhombic perforated graphene structures through molecular dynamics simulations and employing an optimized BPNN model for predictive analysis, it is found that the perforation spacing ratio (IS) has the most significant effect on the Poisson’s ratio of rhombic perforated graphene, while the perforation aspect ratio (AR) and unit cell size (L) have relatively weak influence. The study further investigates the influence of various perforation geometric parameters on the NPR behavior of graphene. It is found that reducing IS and increasing AR can enhance the negative Poisson’s ratio effect. The machine learning predictions closely align with molecular dynamics simulation results, demonstrating the effectiveness and reliability of this approach for Poisson’s ratio prediction. By integrating rhombic perforation design with machine learning technologies, this research provides an efficient framework for optimizing the NPR effect in graphene, and theoretical support for its application in smart materials and flexible electronics.